Finite Group Databasebeta

← #14327479

Subgroups — #14327479

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91989C211yesmaximal, characteristic, complemented
2C2×D3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3C4×D5×#67C211yesmaximal, characteristic
4C3×#65765C211yesmaximal, characteristic, complemented
5#11752055C212yesmaximal
6#11752017C212yesmaximal, complemented
7#11751931C212yesmaximal, complemented
8#11751855C211yesmaximal, characteristic, complemented
9Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
10#11751751C211yesmaximal, characteristic, complemented
11#11751747C212yesmaximal, complemented
12#10617179—31nomaximal, Hall
13C22×D3×AGL(1,𝔽5)C2212yes—
14C22×C3×C4×D5C2211yescharacteristic
15C2×D5×#67C2211yescharacteristic
16C2×C4×D3×D5C2211yescharacteristic
17C2×#6763C2212yes—
18#91989—24no—
19C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
20C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
21C2×C4×ΓL(1,𝔽16)C2212yes—
22C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
23C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
25C2×Dic3⋊AGL(1,𝔽5)C2212yes—
26C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
27C2×Dic3×AGL(1,𝔽5)C2212yes—
28D3×C4⋊AGL(1,𝔽5)—24no—
29C4×#1220C411yescharacteristic, complemented
30C4×C5×#67C411yescharacteristic, complemented
31#91552C411yescharacteristic, complemented
32Dic5×#67C411yescharacteristic, complemented
33D5×#217C2211yescharacteristic
34D5×(C2×D3)⋊C4C2211yescharacteristic
35#91444C411yescharacteristic, complemented
36C4×#1202C411yescharacteristic, complemented
37#91440C411yescharacteristic, complemented
38C4×#1201C411yescharacteristic, complemented
39D5×Dic3⋊C4C2211yescharacteristic
40C4×D5×Dic3C2211yescharacteristic
41C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
45(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
46#74012—51nomaximal, Hall
47C2×#4130—31no—
48C22×C4⋊AGL(1,𝔽5)—31no—
49C4×D4×D5—31no—
50#65779—32no—
51#65765—31no—
52#65765D311yescharacteristic, complemented
53#65711—32no—
54#65700—32no—
55C22⋊C4×AGL(1,𝔽5)—32no—
56#65689—31no—
57C4×C4⋊AGL(1,𝔽5)—31no—
58C23×C3×D5C2311yescharacteristic
59C22×D3×D5C2311yescharacteristic
60C22×ΓL(1,𝔽16)C2312yes—
61C22×ΓL(1,𝔽16)C2312yes—
62C22×C3×AGL(1,𝔽5)C2312yes—
63C22×C3×AGL(1,𝔽5)C2312yes—
64C2×D3×AGL(1,𝔽5)—24no—
65C2×D3×AGL(1,𝔽5)—24no—
66C2×D3×AGL(1,𝔽5)—42no—
67C22×C3×C4×C5C2×C411yescharacteristic, complemented
68C2×#1220C2×C411yescharacteristic
69C2×C4×D15C2×C411yescharacteristic
70C2×C5×#67C2×C411yescharacteristic
71C2×C4×C5×D3C2×C411yescharacteristic
72C22×C3×Dic5C2×C411yescharacteristic, complemented
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5C2×C411yescharacteristic, complemented
76C2×C3×C4×D5C2×C411yescharacteristic, complemented
77C2×C3×C4×D5C2311yescharacteristic
78C2×C3×C4×D5C2311yescharacteristic
79D5×#67—22no—
80D5×#67—22no—
81C2×#1202C2×C411yescharacteristic
82C2×#1201C2×C411yescharacteristic
83C2×#1200C2×C411yescharacteristic
84C2×D3×Dic5C2×C411yescharacteristic
85C2×D5×Dic3C2311yescharacteristic
86C2×D5×Dic3C2311yescharacteristic
87C2×D5×Dic3C2311yescharacteristic
88C4×D3×D5—22no—
89C4×D3×D5—22no—
90#6763—24no—
91C4⋊ΓL(1,𝔽16)—22no—
92C4⋊ΓL(1,𝔽16)D414yescomplemented
93C4×ΓL(1,𝔽16)—24no—
94C3×C22⋊AGL(1,𝔽5)—42no—
95C3×C4⋊AGL(1,𝔽5)—22no—
96C3×C4⋊AGL(1,𝔽5)—22no—
97Dic3⋊AGL(1,𝔽5)—24no—
98(C2×D3)⋊AGL(1,𝔽5)—24no—
99Dic3×AGL(1,𝔽5)—42no—
100#6719C2×C411yescharacteristic, complemented
101#6714C2×C411yescharacteristic
102#6712C2×C411yescharacteristic, complemented
103C4×Dic15C2×C411yescharacteristic, complemented
104C5×#217C2×C411yescharacteristic, complemented
105C5×(C2×D3)⋊C4C2×C411yescharacteristic
106C5×Dic3⋊C4C2×C411yescharacteristic, complemented
107C4×C5×Dic3C2×C411yescharacteristic, complemented
108Dic3⋊Dic5C2×C411yescharacteristic, complemented
109#6669C2×C411yescharacteristic, complemented
110#6667C2×C411yescharacteristic
111(C2×D3)⋊Dic5C2×C411yescharacteristic
112#6665C2×C411yescharacteristic, complemented
113#6665C2×C411yescharacteristic, complemented
114Dic3×Dic5C2×C411yescharacteristic, complemented
115Dic3×Dic5C2×C411yescharacteristic, complemented
116C2×C4×#67—51no—
117C2×#926—51no—
118C2×D3×C4⋊C4—51no—
119C3×#380—51no—
120#4987—51no—
121#4977—51no—
122Dic3×C4⋊C4—51no—
123#4956—52no—
124#4944—52no—
125#4666—52no—
126#4652—52no—
127C23×AGL(1,𝔽5)—32no—
128C2×D4×D5—31no—
129C22×C4×D5—31no—
130C22×C4×D5C2×D311yescharacteristic
131C2×C22⋊AGL(1,𝔽5)—32no—
132C2×C22⋊AGL(1,𝔽5)—32no—
133C2×C22⋊AGL(1,𝔽5)C2×D312yes—
134#4130—64no—
135C2×C4⋊AGL(1,𝔽5)—31no—
136C2×C4⋊AGL(1,𝔽5)—32no—
137C2×C4⋊AGL(1,𝔽5)—31no—
138C2×C4⋊AGL(1,𝔽5)—64no—
139C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
140C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
141C2×C4×AGL(1,𝔽5)—32no—
142C2×C4×AGL(1,𝔽5)—32no—
143C4×C5×D4—31no—
144D4×Dic5—31no—
145C4×C22⋊D5—31no—
146C4×C22⋊D5—31no—
147#4039—31no—
148D5×C4⋊C4—31no—
149#4027—31no—
150#4027—31no—
151D5×C22⋊C4—31no—
152D5×C22⋊C4—31no—
153C4×D20—31no—
154C42×D5—31no—
155(C2×AGL(1,𝔽5))⋊C4—32no—
156(C2×AGL(1,𝔽5))⋊C4—32no—
157(C2×AGL(1,𝔽5))⋊C4—32no—
158(C2×AGL(1,𝔽5))⋊C4—32no—
159(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
160#2352—151noSylow
161C23×C3×C5C22×C411yescharacteristic
162C22×D15C22×C411yescharacteristic
163C22×C5×D3C22×C411yescharacteristic
164C22×C3×D5—21no—
165C22×C3×D5—21no—
166C22×C3×D5—21no—
167C22×C3×D5—21no—
168C22×C3×D5—21no—
169C22×C3×D5—21no—
170C22×C3×D5C22×C411yescharacteristic
171C22×C3×D5C2411yescharacteristic
172C2×D3×D5—21no—
173C2×D3×D5—21no—
174C2×D3×D5—21no—
175C2×D3×D5—21no—
176C2×D3×D5#4112yes—
177C2×D3×D5#4112yes—
178C2×ΓL(1,𝔽16)—22no—
179C2×ΓL(1,𝔽16)—22no—
180C2×ΓL(1,𝔽16)—22no—
181C2×ΓL(1,𝔽16)—22no—
182C2×ΓL(1,𝔽16)—22no—
183C2×ΓL(1,𝔽16)C2×D414yes—
184C2×C3×AGL(1,𝔽5)—22no—
185C2×C3×AGL(1,𝔽5)—22no—
186C2×C3×AGL(1,𝔽5)—22no—
187C2×C3×AGL(1,𝔽5)—22no—
188C2×C3×AGL(1,𝔽5)—22no—
189C2×C3×AGL(1,𝔽5)—22no—
190D3×AGL(1,𝔽5)—48no—
191C2×C3×C4×C5—22no—
192C2×C3×C4×C5C22×C411yescharacteristic
193C2×C3×C4×C5C22×C411yescharacteristic
194#1220—22no—
195C2×Dic15C22×C411yescharacteristic
196C2×Dic15C22×C411yescharacteristic
197C2×Dic15C22×C411yescharacteristic
198C4×D15—22no—
199C5×#67—22no—
200C2×C5×Dic3C22×C411yescharacteristic
201C2×C5×Dic3C22×C411yescharacteristic
202C2×C5×Dic3C22×C411yescharacteristic
203C4×C5×D3—22no—
204C2×C3×Dic5—22no—
205C2×C3×Dic5C22×C411yescharacteristic
206C2×C3×Dic5C22×C411yescharacteristic
207C3×C4×D5—21no—
208C3×C4×D5—21no—
209C3×C4×D5—22no—
210C3×C4×D5—22no—
211C3×C4×D5C2×D412yes—
212C3×C4×D5#4112yes—
213#1202—22no—
214#1201—22no—
215#1200—22no—
216D3×Dic5—22no—
217D5×Dic3—21no—
218D5×Dic3—21no—
219D5×Dic3—21no—
220D5×Dic3—21no—
221D5×Dic3—21no—
222D5×Dic3—21no—
223C23×C3×C4—51no—
224C22×#67—51no—
225C22×C4×D3—51no—
226C22×C4×D3—52no—
227C2×C3×C4⋊C4—51no—
228C2×C3×C4⋊C4—51no—
229C2×C3×C22⋊C4—52no—
230C2×#217—51no—
231C2×#217—52no—
232C4×#67—51no—
233C4×#67—51no—
234C4×#67—51no—
235C4×#67—51no—
236C4×#67—51no—
237C4×#67—51no—
238C4×#67—51no—
239C4×#67AGL(1,𝔽5)11yescharacteristic, complemented
240C2×(C2×D3)⋊C4—51no—
241C2×(C2×D3)⋊C4—52no—
242#926—104no—
243C2×C4⋊Dic3—51no—
244C2×C4⋊Dic3—51no—
245C2×Dic3⋊C4—51no—
246C2×Dic3⋊C4—52no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3—52no—
249C2×C4×Dic3—52no—
250D3×C4⋊C4—104no—
251C3×#95—52no—
252C3⋊#95—52no—
253C3⋊#95—52no—
254C3⋊#95—52no—
255C3⋊#95—52no—
256C23×D5—31no—
257C23×D5C22×D311yescharacteristic
258C22×AGL(1,𝔽5)—32no—
259C22×AGL(1,𝔽5)—32no—
260C22×AGL(1,𝔽5)—64no—
261C22×AGL(1,𝔽5)—64no—
262C22×AGL(1,𝔽5)—122no—
263C22×AGL(1,𝔽5)C22×D312yes—
264C22×AGL(1,𝔽5)C22×D312yes—
265C2×C5×D4—31no—
266C22×C4×C5—31no—
267C22×C4×C5C4×D311yescharacteristic, complemented
268C2×C22⋊D5—31no—
269C2×C22⋊D5—31no—
270C22×Dic5—31no—
271C22×Dic5C4×D311yescharacteristic, complemented
272D4×D5—62no—
273D4×D5—62no—
274C2×D20—31no—
275C2×C4×D5—22no—
276C2×C4×D5—22no—
277C2×C4×D5—31no—
278C2×C4×D5—31no—
279C2×C4×D5—31no—
280C2×C4×D5—31no—
281C2×C4×D5—31no—
282C2×C4×D5—62no—
283C2×C4×D5—62no—
284C2×C4×D5C4×D311yescharacteristic, complemented
285C2×C4×D5C4×D311yescharacteristic, complemented
286C2×C4×D5C22×D311yescharacteristic
287C2×C4×D5C22×D311yescharacteristic
288C22⋊AGL(1,𝔽5)—42no—
289C22⋊AGL(1,𝔽5)—64no—
290C22⋊AGL(1,𝔽5)—64no—
291C4⋊AGL(1,𝔽5)—22no—
292C4⋊AGL(1,𝔽5)—22no—
293C4⋊AGL(1,𝔽5)—34no—
294C4⋊AGL(1,𝔽5)—64no—
295C4⋊AGL(1,𝔽5)—62no—
296C4×AGL(1,𝔽5)—64no—
297C4×AGL(1,𝔽5)—122no—
298C5×C4⋊C4—31no—
299C5×C22⋊C4—31no—
300C5×C22⋊C4—31no—
301C42×C5—31no—
302C22⋊Dic5—31no—
303C22⋊Dic5—31no—
304#685—31no—
305#685—31no—
306#685—31no—
307#685—31no—
308C4⋊Dic5—31no—
309#683—31no—
310#683—31no—
311C4×Dic5—31no—
312C4×Dic5—31no—
313C4×Dic5—31no—
314C2×C4×D4—151no—
315C2×#117—151no—
316C22×C4⋊C4—151no—
317#388—152no—
318#387—152no—
319#386—152no—
320#382—151no—
321#380—51no—
322#380—151no—
323C4×C4⋊C4—151no—
324C4×C22⋊C4—152no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5C23×C411yescharacteristic
329C2×D15—21no—
330C2×D15—21no—
331C2×D15#11712yescomplemented
332C2×C5×D3—21no—
333C2×C5×D3—21no—
334C2×C5×D3#11712yescomplemented
335C2×C3×D5—21no—
336C2×C3×D5—21no—
337C2×C3×D5—21no—
338C2×C3×D5—41no—
339C2×C3×D5—41no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C2×C3×D5C22×D411yescharacteristic
343C2×C3×D5C2×#4111yescharacteristic
344C2×C3×D5C2×#4111yescharacteristic
345C2×C3×D5C2×#4111yescharacteristic
346C2×C3×D5H(5,𝔽2)11yescharacteristic
347C2×C3×D52−1+411yescharacteristic
348D3×D5—22no—
349D3×D5—22no—
350D3×D5—22no—
351D3×D5—22no—
352ΓL(1,𝔽16)—24no—
353ΓL(1,𝔽16)—42no—
354C3×AGL(1,𝔽5)—42no—
355C3×AGL(1,𝔽5)—42no—
356C3×C4×C5—21no—
357C3×C4×C5C4×D412yes—
358Dic15—21no—
359Dic15—21no—
360Dic15—21no—
361C3×Dic5—21no—
362C3×Dic5C4×D412yes—
363C5×Dic3—21no—
364C5×Dic3—21no—
365C5×Dic3—21no—
366C24×C3—51no—
367C23×D3—51no—
368C22×C3×C4—51no—
369C22×C3×C4—51no—
370C22×C3×C4—51no—
371C22×C3×C4—51no—
372C22×C3×C4—51no—
373C22×C3×C4—52no—
374C22×C3×C4—52no—
375C22×C3×C4—102no—
376C22×C3×C4—102no—
377C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
378C2×#67—51no—
379C2×#67—51no—
380C2×#67—51no—
381C2×#67—102no—
382C2×#67—102no—
383C2×#67C2×AGL(1,𝔽5)11yescharacteristic
384C22×Dic3—52no—
385C22×Dic3—51no—
386C22×Dic3—51no—
387C22×Dic3—51no—
388C22×Dic3—52no—
389C2×C4×D3—51no—
390C2×C4×D3—51no—
391C2×C4×D3—51no—
392C2×C4×D3—102no—
393C2×C4×D3—102no—
394C2×C4×D3—104no—
395C2×C4×D3—104no—
396C2×C4×D3—202no—
397C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
398C3×C4⋊C4—102no—
399C3×C4⋊C4—102no—
400C3×C22⋊C4—202no—
401#217—51no—
402#217—51no—
403#217—51no—
404#217—104no—
405#217C2×AGL(1,𝔽5)11yescharacteristic, complemented
406(C2×D3)⋊C4—51no—
407(C2×D3)⋊C4—51no—
408(C2×D3)⋊C4—51no—
409(C2×D3)⋊C4—104no—
410(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
411C4⋊Dic3—54no—
412C4⋊Dic3—102no—
413Dic3⋊C4—51no—
414Dic3⋊C4—51no—
415Dic3⋊C4—51no—
416Dic3⋊C4—104no—
417Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
418C4×Dic3—51no—
419C4×Dic3—51no—
420C4×Dic3—51no—
421C4×Dic3—104no—
422C4×Dic3—202no—
423C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
424C23×C5—31no—
425C23×C5C2×C4×D311yescharacteristic
426C22×D5—21no—
427C22×D5—21no—
428C22×D5—21no—
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—21no—
432C22×D5—31no—
433C22×D5—32no—
434C22×D5—32no—
435C22×D5—61no—
436C22×D5—61no—
437C22×D5—61no—
438C22×D5—61no—
439C22×D5C2×C4×D311yescharacteristic
440C22×D5C23×D311yescharacteristic
441C2×AGL(1,𝔽5)—22no—
442C2×AGL(1,𝔽5)—22no—
443C2×AGL(1,𝔽5)—22no—
444C2×AGL(1,𝔽5)—22no—
445C2×AGL(1,𝔽5)—22no—
446C2×AGL(1,𝔽5)—22no—
447C2×AGL(1,𝔽5)—34no—
448C2×AGL(1,𝔽5)—62no—
449C2×AGL(1,𝔽5)—62no—
450C2×AGL(1,𝔽5)—62no—
451C2×AGL(1,𝔽5)—62no—
452C2×AGL(1,𝔽5)—62no—
453C2×AGL(1,𝔽5)—128no—
454C5×D4—62no—
455C2×C4×C5—22no—
456C2×C4×C5—31no—
457C2×C4×C5—31no—
458C2×C4×C5—31no—
459C2×C4×C5—62no—
460C2×C4×C5C2×C4×D311yescharacteristic
461C2×C4×C5C2×C4×D311yescharacteristic
462C22⋊D5—62no—
463C22⋊D5—62no—
464C2×Dic5—22no—
465C2×Dic5—31no—
466C2×Dic5—31no—
467C2×Dic5—31no—
468C2×Dic5—62no—
469C2×Dic5C2×C4×D311yescharacteristic
470C2×Dic5C2×C4×D311yescharacteristic
471D20—62no—
472C4×D5—21no—
473C4×D5—21no—
474C4×D5—22no—
475C4×D5—22no—
476C4×D5—61no—
477C4×D5—61no—
478C4×D5—61no—
479C4×D5—61no—
480C4×D5—61no—
481C4×D5—61no—
482C4×D5—62no—
483C4×D5—62no—
484C4×D5D3×D412yes—
485C4×D5#23712yes—
486C22×D4—151no—
487C23×C4—51no—
488C23×C4—151no—
489C23×C4—152no—
490C4×D4—31no—
491C4×D4—151no—
492C4×D4—151no—
493C4×D4—151no—
494C4×D4—151no—
495C4×D4—151no—
496C4×D4—151no—
497C4×D4—151no—
498#117—304no—
499C2×C4⋊C4—51no—
500C2×C4⋊C4—51no—
501C2×C4⋊C4—151no—
502C2×C4⋊C4—151no—
503C2×C4⋊C4—152no—
504C2×C4⋊C4—151no—
505C2×C4⋊C4—304no—
506C2×C22⋊C4—52no—
507C2×C22⋊C4—151no—
508C2×C22⋊C4—151no—
509C2×C22⋊C4—152no—
510C2×C22⋊C4—152no—
511C2×C42—151no—
512C2×C42—152no—
513C2×C42—152no—
514#95—52no—
515#95—152no—
516#95—152no—
517#95—152no—
518#95—152no—
519C2×C3×C5—41no—
520C2×C3×C5C2×#11711yescharacteristic
521C2×C3×C5C2×C4×D411yescharacteristic
522C2×C3×C5#52011yescharacteristic
523D15—22no—
524C3×D5—41no—
525C3×D5#54611yescharacteristic
526C3×D5#54811yescharacteristic
527C3×D5#55211yescharacteristic
528C3×D5#55311yescharacteristic
529C5×D3—22no—
530C23×C3—51no—
531C23×C3—51no—
532C23×C3—101no—
533C23×C3—101no—
534C23×C3—101no—
535C23×C3—101no—
536C23×C3—101no—
537C23×C3—101no—
538C23×C3C22×AGL(1,𝔽5)11yescharacteristic
539C22×D3—51no—
540C22×D3—52no—
541C22×D3—52no—
542C22×D3—101no—
543C22×D3—101no—
544C22×D3—101no—
545C22×D3—101no—
546C22×D3C22×AGL(1,𝔽5)11yescharacteristic
547C2×C3×C4—22no—
548C2×C3×C4—51no—
549C2×C3×C4—52no—
550C2×C3×C4—52no—
551C2×C3×C4—51no—
552C2×C3×C4—102no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—102no—
556C2×C3×C4—102no—
557C2×C3×C4—102no—
558C2×C3×C4—102no—
559C2×C3×C4—102no—
560C2×C3×C4—102no—
561C2×C3×C4—102no—
562C2×C3×C4—102no—
563C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
564C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
565#67—22no—
566#67—102no—
567#67—102no—
568#67—102no—
569C2×Dic3—54no—
570C2×Dic3—51no—
571C2×Dic3—51no—
572C2×Dic3—51no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3—102no—
580C2×Dic3—102no—
581C2×Dic3—102no—
582C2×Dic3—102no—
583C2×Dic3—102no—
584C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
585C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
586C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
587C4×D3—22no—
588C4×D3—102no—
589C4×D3—102no—
590C4×D3—102no—
591C4×D3—208no—
592C22×C5—21no—
593C22×C5—21no—
594C22×C5—21no—
595C22×C5—32no—
596C22×C5—61no—
597C22×C5—61no—
598C22×C5C22×C4×D311yescharacteristic
599C2×D5—21no—
600C2×D5—21no—
601C2×D5—21no—
602C2×D5—32no—
603C2×D5—41no—
604C2×D5—41no—
605C2×D5—41no—
606C2×D5—41no—
607C2×D5—61no—
608C2×D5—61no—
609C2×D5—62no—
610C2×D5—62no—
611C2×D5—62no—
612C2×D5—62no—
613C2×D5C2×D3×D411yescharacteristic
614C2×D5C2×#23711yescharacteristic
615C2×D5#100411yescharacteristic
616C2×D5#100711yescharacteristic
617C2×D5D3×#4111yescharacteristic
618C2×D5D3×#4111yescharacteristic
619AGL(1,𝔽5)—42no—
620AGL(1,𝔽5)—42no—
621AGL(1,𝔽5)—64no—
622AGL(1,𝔽5)—122no—
623C4×C5—21no—
624C4×C5—61no—
625C4×C5—61no—
626C4×C5—61no—
627C4×C5#67⋊C412yes—
628Dic5—21no—
629Dic5—61no—
630Dic5—61no—
631Dic5—61no—
632Dic5#67⋊C412yes—
633C24—51no—
634C24—151no—
635C2×D4—31no—
636C2×D4—151no—
637C2×D4—151no—
638C2×D4—151no—
639C2×D4—302no—
640C2×D4—302no—
641C22×C4—31no—
642C22×C4—51no—
643C22×C4—51no—
644C22×C4—51no—
645C22×C4—51no—
646C22×C4—51no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—102no—
650C22×C4—102no—
651C22×C4—151no—
652C22×C4—151no—
653C22×C4—151no—
654C22×C4—151no—
655C22×C4—151no—
656C22×C4—152no—
657C22×C4—151no—
658C22×C4—152no—
659C22×C4—302no—
660C22×C4—302no—
661C22×C4—304no—
662C22×C4—304no—
663C22×C4—602no—
664C22×C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
665C4⋊C4—31no—
666C4⋊C4—102no—
667C4⋊C4—102no—
668C4⋊C4—151no—
669C4⋊C4—151no—
670C4⋊C4—154no—
671C4⋊C4—151no—
672C4⋊C4—302no—
673C4⋊C4—304no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—151no—
677C22⋊C4—151no—
678C22⋊C4—151no—
679C22⋊C4—151no—
680C22⋊C4—151no—
681C22⋊C4—151no—
682C22⋊C4—202no—
683C22⋊C4—304no—
684C22⋊C4—304no—
685C42—31no—
686C42—151no—
687C42—151no—
688C42—151no—
689C42—304no—
690C42—602no—
691C3×C5#235211yescharacteristic, complemented, Hall
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—51no—
696C22×C3—51no—
697C22×C3—51no—
698C22×C3—51no—
699C22×C3—51no—
700C22×C3—51no—
701C22×C3—101no—
702C22×C3—101no—
703C22×C3—101no—
704C22×C3—201no—
705C22×C3—201no—
706C22×C3—201no—
707C22×C3—201no—
708C22×C3C23×AGL(1,𝔽5)11yescharacteristic
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—52no—
712C2×D3—102no—
713C2×D3—102no—
714C2×D3—102no—
715C2×D3—102no—
716C2×D3—101no—
717C2×D3—101no—
718C2×D3#413012yescomplemented
719C3×C4—21no—
720C3×C4—52no—
721C3×C4—101no—
722C3×C4—202no—
723C3×C4—202no—
724C3×C4D4×AGL(1,𝔽5)12yes—
725Dic3—21no—
726Dic3—21no—
727Dic3—21no—
728Dic3—104no—
729Dic3—101no—
730Dic3—101no—
731Dic3—101no—
732Dic3—202no—
733C2×C5—41no—
734C2×C5—62no—
735C2×C5C2×#67⋊C411yescharacteristic
736C2×C5#550411yescharacteristic
737C2×C5D3×#11711yescharacteristic
738D5—41no—
739D5—62no—
740D5#561211yescharacteristic
741D5#561411yescharacteristic
742D5#563311yescharacteristic
743D5#563911yescharacteristic
744C23—31no—
745C23—51no—
746C23—51no—
747C23—101no—
748C23—101no—
749C23—101no—
750C23—101no—
751C23—101no—
752C23—101no—
753C23—152no—
754C23—152no—
755C23—151no—
756C23—301no—
757C23—301no—
758C23—301no—
759C23—301no—
760C23C2×D3×AGL(1,𝔽5)11yescharacteristic
761D4—62no—
762D4—302no—
763D4—302no—
764D4—302no—
765C2×C4—22no—
766C2×C4—31no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—51no—
770C2×C4—52no—
771C2×C4—52no—
772C2×C4—51no—
773C2×C4—62no—
774C2×C4—102no—
775C2×C4—101no—
776C2×C4—101no—
777C2×C4—102no—
778C2×C4—102no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—102no—
782C2×C4—102no—
783C2×C4—102no—
784C2×C4—102no—
785C2×C4—154no—
786C2×C4—151no—
787C2×C4—151no—
788C2×C4—151no—
789C2×C4—302no—
790C2×C4—302no—
791C2×C4—301no—
792C2×C4—301no—
793C2×C4—301no—
794C2×C4—301no—
795C2×C4—301no—
796C2×C4—301no—
797C2×C4—302no—
798C2×C4—302no—
799C2×C4—302no—
800C2×C4—302no—
801C2×C4—302no—
802C2×C4—302no—
803C2×C4—608no—
804C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
805C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
806C2×C3—41no—
807C2×C3—51no—
808C2×C3—51no—
809C2×C3—51no—
810C2×C3—51no—
811C2×C3—201no—
812C2×C3C2×#413011yescharacteristic
813C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
814C2×C3#6626611yescharacteristic
815D3—22no—
816D3—102no—
817C5#7401211yescharacteristic, complemented, Sylow
818C22—21no—
819C22—21no—
820C22—21no—
821C22—32no—
822C22—51no—
823C22—51no—
824C22—51no—
825C22—51no—
826C22—51no—
827C22—51no—
828C22—61no—
829C22—61no—
830C22—101no—
831C22—101no—
832C22—101no—
833C22—152no—
834C22—201no—
835C22—201no—
836C22—201no—
837C22—201no—
838C22—302no—
839C22—302no—
840C22—302no—
841C22—302no—
842C22—301no—
843C22—301no—
844C22C22×D3×AGL(1,𝔽5)11yescharacteristic
845C4—21no—
846C4—52no—
847C4—61no—
848C4—61no—
849C4—61no—
850C4—101no—
851C4—202no—
852C4—202no—
853C4—304no—
854C4—301no—
855C4—301no—
856C4—301no—
857C4—602no—
858C4#67⋊AGL(1,𝔽5)12yes—
859C3#1061717911yescharacteristic, complemented, Sylow
860C2—41no—
861C2—51no—
862C2—51no—
863C2—51no—
864C2—51no—
865C2—62no—
866C2—201no—
867C2—302no—
868C2D3×#413011yescharacteristic
869C2#1175683611yescharacteristic
870C2C2×#67⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC2×D5×#67C22
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2352
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#91989C2semidirect
2. C2×D3×C4⋊AGL(1,𝔽5)C2semidirect
4. C3×#65765C2semidirect
6. #11752017C2semidirect
7. #11751931C2semidirect
8. #11751855C2semidirect
9. Dic3×C4⋊AGL(1,𝔽5)C2semidirect
10. #11751751C2semidirect
11. #11751747C2semidirect
29. C4×#1220C4semidirect
30. C4×C5×#67C4semidirect
31. #91552C4semidirect
32. Dic5×#67C4semidirect
35. #91444C4semidirect
36. C4×#1202C4semidirect
37. #91440C4semidirect
38. C4×#1201C4semidirect
52. #65765D3semidirect
67. C22×C3×C4×C5C2×C4semidirect
72. C22×C3×Dic5C2×C4semidirect
75. C2×C3×C4×D5C2×C4semidirect
76. C2×C3×C4×D5C2×C4semidirect
92. C4⋊ΓL(1,𝔽16)D4semidirect
100. #6719C2×C4semidirect
102. #6712C2×C4semidirect
103. C4×Dic15C2×C4semidirect
104. C5×#217C2×C4semidirect
106. C5×Dic3⋊C4C2×C4semidirect
107. C4×C5×Dic3C2×C4semidirect
108. Dic3⋊Dic5C2×C4semidirect
109. #6669C2×C4semidirect
112. #6665C2×C4semidirect
113. #6665C2×C4semidirect
114. Dic3×Dic5C2×C4semidirect
115. Dic3×Dic5C2×C4semidirect
239. C4×#67AGL(1,𝔽5)semidirect
267. C22×C4×C5C4×D3semidirect
271. C22×Dic5C4×D3semidirect
284. C2×C4×D5C4×D3semidirect
285. C2×C4×D5C4×D3semidirect
331. C2×D15#117semidirect
334. C2×C5×D3#117semidirect
377. C22×C3×C4C2×AGL(1,𝔽5)semidirect
405. #217C2×AGL(1,𝔽5)semidirect
417. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
423. C4×Dic3C2×AGL(1,𝔽5)semidirect
664. C22×C4D3×AGL(1,𝔽5)semidirect
691. C3×C5#2352semidirect
718. C2×D3#4130semidirect
817. C5#74012semidirect
859. C3#10617179semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#919892
C2×D3×C4⋊AGL(1,𝔽5)2
C4×D5×#672
C3×#657652
#117520552
#117520172
#117519312
#117518552
Dic3×C4⋊AGL(1,𝔽5)2
#117517512
#117517472
#106171793
#740125